How can I make an object face or locate to the active camera?
Consider a [track to] constraint which rotates the bones







You can track to the camera or some object like two rectangles next to each other lets call them a pair of eye trackables, similar in placement to a pair of eye glasses. Depicted above in the animation is an example. Left eye tracks left point, right eye tracks right point.  The points are eye distance apart.  At a far distance the eye trackables cause the eyes to rotate and be nearly parallel.  At a close distance the this can prevent crossed eye problem.  Some blender people might say the having a separate eye trackables is more flexible than tracking to the camera.  You can move the trackables independent of the camera.
Consider searching Blender Facial Rig Eyes